Stellenbosch University
Applied Mathematics

Announcements - Check here regularly for updates

  • Because of the COVID-19 outbreak, the next block will be presented online. See the box below for details.
  • Marks for tut 01 and tut 01 available here here.
  • Assignment 01 is available below. Check back regularly for updates corrections.
  • Notes from the first block available here.
  • Tutorials 1 and 2, plus their solutions, are available below.

Changes to programme following COVID-19 SU precautions

  • Classes for the 2nd term, including TW876, will be presented online via SUNLearn.
  • If you do not have access to this course on SUNLearn (i.e., you have not registered for the module) then you will need to do so AS SOON AS POSSIBLE. Contact your graduate programme coordinator if this is a problem.
  • The deadline for Assignment 01 remains the same (28/04) but the assignment should be submitted ELECTRONICALLY via SUNLearn as a SINGLE PDF file. (If you do not have access to a scanner, taking a photograph of hand-written work is acceptable as long as it is legible.)
  • If you had to leave campus and do not have access to MATLAB or Python, please contact me IMMEDIATELY.
  • The dates for the next block remain the same, and (although online) the structure will be similar to the first block (i.e., a mixture of lectures and tutorials). We are investigating tools to facilitate online assistance for the tutorials. I hope to post a detailed list of the topics (and their section numbers in the textbook) by the end of this week (27 March).

MATLAB

  • This course assumes some previous experience with MATLAB (or Python).
  • MATLAB is now FREE for all SU students! Download instructions here.
    Alternatively, you can use MATLAB in your browser! (But this may be slower.)
  • I strongly recommend completing the (free) online MATLAB Onramp as a refresher.

Lecturer

Dates and venues

  • 2nd March (9h00-17h00) - Venues: Paul Sauer 1006 (morning) and NARGA A (afternoon)
  • 3rd March (9h00-17h00) - Venues: Paul Sauer 1006 (morning) and FIRGA S203 (afternoon)
  • 28-30 April (9h00-17h00) - Venue: online (SUNLearn).

Module Framework

  • The module framework is available here.

Notes

Tutorials and Assignments

Tutorial Due date Solutions
Tutorial 1 02/03/2020 Solutions 1
Tutorial 2 03/03/2020 Solutions 2
Assignment Due date Solutions
Assignment 1
28/04/2020 Solutions 1

Schedule (tentative and subject to change)

Day 1 (Chapter 1 and 2)
  • Fundamentals of Scientific computing
  • Existence and uniqueness of solutions to linear systems
  • Vector and matrix norms
  • Conditioning of linear systems
Day 2 (Chapter 2 cont.) Day 3: (Chapter 3)
  • Least squares problems
  • Normal equations
  • QR Factorization
  • Householder transformation
  • Givens rotations
  • Gram-Schmidt orthogonalisation
Day 4: (Chapter 4)
  • Review of eigenvalues, eigenvectors, diagonalization, similarity transforms
  • Power iteration and its variants
  • Rayleigh-quotient iteration
  • QR iteration
  • Some implementation details of QR iteration, Hessenberg factorization
  • Arnoldi and Lanczos algorithms
Day 5: (Chapter 11)
  • Model problem from finite difference
  • Fixed point iterations and splitting methods
  • Jacobi, Gauss-Seidel, SOR iterations
  • Incomplete LU and Cholesky
  • Method of steepest descent
  • Method of conjugate gradients
  • Pre-conditioning
  • MINRES and GMRES